In many video applications it is desirable to convert a digital signal from one sampling rate to another, according to the format requirements of different devices. The conversion of video signals between composite and component formats requires an encoder or a decoder, depending upon the direction of the conversion, and a sampling rate converter.
In such a conversion polyphase filters are used to calculate data values for the signal at times other than the initial sampling times, which requires a separate filter for each sample subphase. However, component and composite sampling rates do not have simple integer ratios between the sampling frequencies. Thus, large finite impulse response (FIR) filters, mainly implemented in polyphase structure, are required to interpolate and decimate the input signal to achieve the desired sampling rate.
Conventional sampling rate converters are implemented in the component domain. This requires a separate complex rate converter for each of the three components of the signal and very large and complex low-pass filters.
FIGS. 1 and 2 illustrate a conventional sampling rate conversion from 4:2:2 with a sampling frequency F.sub.s of 13.5 MHz to 4fsc with a converted sampling frequency F.sub.c of 14.3 MHz. The conventional transcoder for this conversion is illustrated in FIG. 2. FIG. 1 illustrates the steps through the conversion process, in which the signal is interpolated at a 35:1 rate and a large polyphase FIR filter is used to remove unwanted bands in the component domain. The signal is then clocked out of the polyphase filter at the 14.3 MHz rate.
This approach presents a considerable problem in terms of the design of the required linear phase low-pass filter to meet the frequency domain specifications. The minimum length L of a linear low-pass FIR filter required to meet the frequency domain specifications is given by the following equation: ##EQU1## where .delta..sub.p and .delta..sub.s are the passband and stopband ripples, respectively, and .DELTA.F is the transition bandwidth.
If the maximum passband ripple is assumed to be 0.02 dB and the maximum stopband attenuation is assumed to be 60 dB, .delta..sub.p and .delta..sub.s become 0.0023 and 0.001, respectively. For a conventional sampling rate converter the transition bandwidth .DELTA.F can be seen to be .DELTA.F=(6.75-5.75)/(13.5.times.35)=0.02116, which results in a filter length L of 1404.
This problem becomes even more acute in the case of conversion to 4fsc with a sampling frequency of 17.7 MHz in the case of the PAL television standard, where the minimum filter length L is greater than 709,000. The complexity and costs associated with such a filter renders the design extremely impractical, if not impossible.